Work Space Limits

Description

Each robot work's environment contains several frames, which has different definitions and limitations. The purpose of the Work Space Limits commands is to defined each frame limitations, and combine them under all of the constraints.

Definitions

The frames are defined as:

• World - universal frame
• Base - #{X,Y,Z,y,p,r}
• Tool - #{X,Y,Z,y,p,r}
• MachineTable - #{X,Y,Z,y,p,r}
• WorkPiece - #{X,Y,Z,y,p,r}

When # represent Cartesian point coordinate.

The robot SetPoint parameter defined as the edge point of the robot's tool. When all frames are set to #{0,0,0,0,0,0}, the robot.SetPoint command will show: SetPoint = P_b, when P_b is the vector to the robot edge relative to it's base (NOT the tool edge).

In general, the robot.SetPoint parameter is calculated as follows:
SetPoint = WorkPiece^-1:MachineTable^-1:Base:P_b:Tool
The relations between the frames and the P_b vector shown here:

Work Space Limits definition

As each frame has it's self limitations, and to define them you should use <Frame>.command, for example:

Base.Xmax = 150
?MachineTable.Zmin
Tool.Zmax = 1230

	NOTE
	If these parameters are referred to without a frame, the parameters are set for the WORLD frame

When a move command is issued, an examination is made to check if the point doesn’t exceed the defined limits.
For Moves and Circle commands, the examination checks that the entire path doesn’t exceed the defined limits. For a Move command, only the final point is examined.

For example:

Limits Examination

In order to examine if a certain point is inside the allowed working area, the robot.SetPoint should be transformed into each frame, and then it should be checked that the transformed point is inside the limits of the frame.

The transformations for each frame calculate by the next table:

Frame	Formula
WorkPiece	CheckPoint = SetPoint = WorkPiece-1:MachineTable-1:Base:Pb:Tool
MachineTable	CheckPoint = WorkPiece:SetPoint = MachineTable-1:Base:Pb:Tool
World	CheckPoint = MachineTable:WorkPiece:SetPoint = Base:Pb:Tool
Base	CheckPoint = Base-1:MachineTable:WorkPiece:SetPoint = Pb:Tool
Tool	CheckPoint = Tool-1:Pb,0-1:Base-1:MachineTable:WorkPiece:SetPoint=Tool-1:Pb,0-1:Pb:Tool

	NOTE
	For the Tool frame, the absolute limits are defined relative to Pb at the time that the Tool frame limits were defined. This position is defined as Pb,0 .

The check protocol start with World frame → Base frame → MachineTable frame → WorkPiece frame → Tool frame,
When each frame coordinates checked from Xmax → Xmin → Ymax → Ymin → Zmax → Zmin

	NOTE
	In case that the movement command isn't valid in any parameter, the program will stop checking, and raise an Error Message

6 Degree Of Freedom (DOF) Robot

Frame	Value	Xmin, Xmax	Ymin, Ymax	Zmin, Zmax
WorkPiece	#{20,70,150,0,90,-90}	-200, 200	-200, 200	-200, 200
MachineTable	#{400,100,0,0,0,0}	0, 400	0, 400	0, 800
Base	#{300,200,1000,0,180,180}	-1000, 1000	-1000, 1000	0, 1000
Tool	#{50,0,0,90, 45, 0}	-200, 200	-200, 200	-200, 200
World	None	-1500, 1500	-1500, 1500	0, 2000

Assume that the desired SetPoint is: #{100,100,0,0,0,0} and that P_b,0 is: #{100,100,900,-45,90,0} - Is it in the work area of the limits?

Frame	Formula	In Limits?
WorkPiece	CheckPoint = SetPoint = : #{100,100,0,0,0,0}	Yes
MachineTable	CheckPoint = WorkPiece:SetPoint = #{20,-30,50,0,90,-90}	No - Ymin
Base	CheckPoint = Base-1:MachineTable:WorkPiece:SetPoint = #{120,130,950,0,90,90}	Yes
Tool	CheckPoint = Tool-1:Pb,0-1:Base-1:MachineTable:WorkPiece:SetPoint = #{30,100,20,0,0,0}	Yes
World	CheckPoint = MachineTable:WorkPiece:SetPoint = #{420,70,50,0,90,-90}	Yes

4 Degree Of Freedom (DOF) Robot

Frame	Value	Xmin, Xmax	Ymin, Ymax	Zmin, Zmax
WorkPiece	#{20, 100, 100, 0}	-100, 250	-300, 30	-200, 200
MachineTable	#{120, 60, 0, 0}	0, 700	0, 500	0, 500
Base	#{0, 0, 0, 0}	-1000, 1000	-1000, 1000	0, 1000
Tool	#{0, 20, 40, 10}	-30, 20	-30, 20	-30, 20
World	None	-1500, 1500	-1500, 1500	0, 2000

Assume that the desired SetPoint is: #{660, -140, -60, 0} and that P_b,0 is: #{780, -100, -100, 0} - Is it in the work area of the limits?

Frame	Formula	In Limits?
WorkPiece	CheckPoint = SetPoint = : #{660, -140, -60, 0}	No- Xmax
MachineTable	CheckPoint = WorkPiece:SetPoint = #{680, -40, 40, 0}	No - Ymin
Base	CheckPoint = Base-1:MachineTable:WorkPiece:SetPoint = #{800, 20, 40, 0}	Yes
Tool	CheckPoint = Tool-1:Pb,0-1:Base-1:MachineTable:WorkPiece:SetPoint = #{20, 100, 100, 0}	No - Ymax and Zmax
World	CheckPoint = MachineTable:WorkPiece:SetPoint = #{800, 20, 40, 0}	Yes

See Also

Links to the commands